One of the important challenges in the philosophy of mathematics is to account for the semantics of sentences that express mathematical propositions while simultaneously explaining our access to their contents. This is Benacerraf’s Dilemma. In this dissertation, I argue that cognitive science furnishes new tools by means of which we can make progress on this problem. The foundation of the solution, I argue, must be an ontologically realist, albeit non-platonist, conception of mathematical reality. The semantic portion of the problem can (...) be addressed by accepting a Chomskyan conception of natural languages and a matching internalist, mentalist and nativist view of semantics. A helpful perspective on the epistemic aspect of the puzzle can be gained by translating Kurt G ̈odel’s neo-Kantian conception of the nature of mathematics and its objects into modern, cognitive terms. (shrink)

We present a series of arguments for logical nativism, focusing mainly on the meaning of disjunction in human languages. We propose that all human languages are logical in the sense that the meaning of linguistic expressions corresponding to disjunction (e.g. English or , Chinese huozhe, Japanese ka ) conform to the meaning of the logical operator in classical logic, inclusive- or . It is highly implausible, we argue, that children acquire the (logical) meaning of disjunction by observing how adults use (...) disjunction. Findings from studies of child language acquisition and from cross-linguistic research invite the conclusion that children do not learn to be logical—it comes naturally to them. (shrink)

Two of the most fundamental questions about language are these: what are languages?; and, what is it to know a given language? Many philosophers who have reflected on these questions have presented answers that attribute a central role to conventions. In one of its boldest forms such a view runs as follows. Languages are either social entities constituted by networks of social conventions or abstract objects where when a particular community speaks a given language they do so in virtue of (...) the conventions operative within that community. Consequently, for an individual to know a given language is for them to be party to the relevant conventions. Call this view conventionalism. In this article my aim is to evaluate conventionalism. I will argue that although there are linguistic conventions and that they do play an important role in language development and communication conventionalism should be rejected in favour of a more psychologistically orientated position. (shrink)